Question

Graph the exponential function.g(x) = (4/5)^xPlot five points on the graph of the function. Then click on the graph-a-function button.

Answer 1

Step-by-step explanation

We want to graph the given exponential function:

`g(x)=((4)/(5))^x`

To do this, we have to find 5 points that lie on the graph.

Let us solve the function for x = -6, -3, 0, 3, 6:

`\begin{gathered} \Rightarrow x=-6: \\ g(-6)=((4)/(5))^(-6)=3.81 \\ \Rightarrow x=-3: \\ g(-3)=((4)/(5))^(-3)=1.95 \\ \Rightarrow x=0: \\ g(0)=((4)/(5))^0=1 \\ \Rightarrow x=3: \\ g(3)=((4)/(5))^3=0.51 \\ \Rightarrow x=6: \\ g(6)=((4)/(5))^6=0.26 \end{gathered}`

Now, we have five points to plot the graph with:

`\begin{gathered} (-6,3.81) \\ (-3,1.95) \\ (0,1) \\ (3,0.51) \\ (6,0.26) \end{gathered}`

Let us now plot the points and join the line:

That is the graph of the function